This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003641 Number of genera of imaginary quadratic field with discriminant -k, k = A039957(n). (Formerly M0061) 3
 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 4, 1, 2, 1, 2, 2, 1, 1, 4, 2, 1, 2, 1, 4, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 4, 2, 2, 2, 2, 1, 2, 1, 4, 1, 1, 2, 2, 4, 1, 1, 2, 1, 4, 1, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS In other words, this is the number of genera of those imaginary quadratic fields that have a discriminant which is odd and fundamental. The discriminant will be squarefree and of the form -4n+1. - Andrew Howroyd, Jul 25 2018 REFERENCES D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 224-241. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS FORMULA a(n) = 2^(omega(A039957(n)) - 1). - Jianing Song, Jul 24 2018 EXAMPLE a(4) = 2 because -15 = -A039957(4) and the number of genera of the quadratic field with discriminant -15 is 2. - Andrew Howroyd, Jul 25 2018 MATHEMATICA 2^(PrimeNu[Select[Range[1000], Mod[#, 4] == 3 && SquareFreeQ[#]&]] - 1) (* Jean-François Alcover, Jul 25 2019, after Andrew Howroyd *) PROG (PARI) for(n=1, 1000, if(n%4==3 && issquarefree(n), print1(2^(omega(n) - 1), ", "))) \\ Andrew Howroyd, Jul 24 2018 CROSSREFS Cf. A001221 (omega), A003640, A003642, A039957. Sequence in context: A317934 A279848 A001826 * A165190 A025890 A316975 Adjacent sequences:  A003638 A003639 A003640 * A003642 A003643 A003644 KEYWORD nonn AUTHOR EXTENSIONS Name clarified by Jianing Song, Jul 24 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)